Could thermal stresses in a BGA/CGA-system be evaluated from a model intended for a homogeneously bonded assembly?

Abstract

An analytical stress model is developed for the evaluation of thermal stresses in an inhomogeneously bonded assembly of the ball-grid-array (BGA) or column grid array (CGA) type. It is shown that one can get away with employing a simpler model intended for an assembly with a homogeneous bond, if the gaps between the supports (BGA balls or CGA columns) are small, so that the ratio \( \frac{p}{2l} \) of the pitch p (the distance between the joint centers) to the joint widths 2l is below 5, and the product kl of the parameter k of the interfacial shearing stress and half the assembly length l in the equivalent homogeneously bonded assembly is above 2.5. This is indeed the case for actual BGA and CGA systems. This finding can be used also in other areas of engineering, such as, say, mechanical or structural, when there is an intent to simplify the calculations by replacing a model for beams on separate supports by using a model intended for a beam on a continuous elastic foundation.